Ap stats survey project

AP Stats Survey Project Kimberly Loya - Frank Quiroz - Giovanni Hernandez Period. 04 Mr. Eastvedt

Our non-demographic Survey Questions Q1:Did you ever like Pokémon? Q2:Do you watch TV? Q3:Do you own a laptop? Q4:Do you think teachers should assign homework? Q5:Do you own a smartphone? Q6: How many A’s did you have on your report card last semester? Q7:How many times have you had your hair cut in the past year? Q8:How many video games do you own? Q9:How many hours of sleep do you usually get?

Confidence Intervals for means (numerical questions) Equation: Q6: (2.338, 2.95) We are 95% confident that the true mean of A’s on a students report card lies in the above interval. Q7: (3.48, 5.45) We are 95% confident that the true mean of times a student cut their hair in the past year lies between the above interval. Q8: (7.738, 13.142) We are 95% confident that the true mean of video games a student owns lies between the above interval. Q9: (6.853, 7.447) We are 95% confident that the true mean of hours a student sleeps lies between the above interval.

Confidence intervals for proportions (opinion questions) Equation: Q1: (.651, .808) We are 95% confident that the true proportion of agreement to ever liking Pokémon is between the above interval. Q2: (.901, .984) We are 95% confident that the true proportion of responses agreeing to ever watching TV is between the above interval. Q3: (.478, .654) We are 95% confident that the true proportion of students owning a laptop is between the above interval. Q4: (.461, .637) We are 95% confident that the true proportion of students who think teachers should assign homework is between the above interval. Q5: (.606, .771) We are 95% confident that the true proportion of students owning a smartphone lies between the above interval.

Hypotheses tests: Our results VS. Larger study Q2: 1) Null/Alternate Hypotheses Ho: µ= television has an impact on children’s successes Ha: µ≤ = does not have an impact on a child’s success 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted - !0%: we have less than 10% of all students who watch TV -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: 1 Prop Z-Test 4) Do the Math p=.943 (yes) x=115 n=122 z= p hat – p/ √(p(1-p)/n) p=.507 5) Conclusion With such a high p-value there is not enough evidence to suggest that a television in a child’s room impacts their success. We fail to reject the null hypothesis. Agreed with larger study.

Hypotheses tests: Our results VS. Larger study Q3: 1) Null/Alternate Hypotheses Ho: µ= teen girls are more likely to own a laptop than boys of the same age group Ha: µ1≠µ2 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted -10%: we have less than 10% of all students who own laptops -Nearly Normal: we can assume the distribution is evenly distributed 3) Name the Test: 1 Prop Z-Test 4) Do the Math p=.566 (yes) x=69 n=122 z= p hat – p/ √(p(1-p)/n) z=-.0094 p=.496 5) Conclusion With such a high p-value there is not evidence to suggest that teen girls are more likely to own a laptop than boys in the same age group. We fail to reject the null hypothesis. Agreed with larger study.

Hypotheses tests: Our results VS. Larger study Q4: 1) Null/Alternate Hypotheses Ho: µ= homework in some subjects have little to no effect Ha: µ≤ homework in all subjects does have an effect 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted - !0%: we have less than 10% of all students who believe teachers should not give homework -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: 1 Prop Z-Test 4) Do the Math p=.549 (no) x=55 n=122 z= p hat – p/ √(p(1-p)/n) z=-2.179 p=.0147 5) Conclusion With such a low p-value there is evidence to suggest that homework in some subjects does have little to no impact on the student. We reject the null hypothesis with 95% confidence. Disagreed with larger study.

Hypotheses tests: Our results VS. Larger study Q5: 1) Null/Alternate Hypotheses Ho: µ= the purchase of smart phones is increasing Ha: µ≤the purchase is stagnate and they’re being overestimated 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted - !0%: we have less than 10% of all people who own smart phones -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: 1 Prop Z-Test 4) Do the Math p=.689 (no) x=38 n=122 z= p hat – p/ √(p(1-p)/n) z=.0419 p=.311 5) Conclusion With such a high p-value there is not enough evidence to suggest that the purchase of smart phones is increasing. We fail to reject the null hypothesis with 95% confidence. Agreed with larger study.

Hypotheses tests: Our results VS. Larger study Q8: 1) Null/Alternate Hypotheses Ho: µ= video games have an effect on a child’s control over impulse and prevent the brain from developing correctly Ha: µ≤ videos games do not have an effect on a child’s development 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted - !0%: we have less than 10% of all videogames owned -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: T-Test 4) Do the Math x=10.44 Sx=15.23 n=122 CI=95% P( t ≤ X- µ/(s/ √n) (7.7102, 13.017) 5) Conclusion We are 95% confident that the true mean on whether video games have an affect on a child’s development lies in the interval of (7.7102, 13.017)

Hypotheses tests: Our results VS. Larger study Q9: 1) Null/Alternate Hypotheses Ho: µ= the average amount of time people sleep is 8 hours Ha: µ≥ the average amount of time people sleep is less than 8 hours 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted - !0%: we have less than 10% of all time spent asleep -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: T-Test 4) Do the Math x=7.15 Sx=1.674 n=122 CI=95% P( t ≤ X- µ/(s/ √n) (6.85, 7.45) 5) Conclusion We are 95% confident that the true mean on whether the average amount of time people spend asleep is 8 hours lies in the interval (6.48, 7.45).

Links to larger studies Q2: http://www.usatoday.com/news/nation/2005-07-04-too-much-tv_x.htm Q3: http://www.infoplease.com/science/computers/teen-technology-ownership.htm Q4: http://www.teachersatrisk.com/2011/05/28/homework-in-some-subjects-does-little-to--no-impact/ Q5: http://www.email-marketing-reports.com/wireless-mobile/smartphone-statistics.htm Q8: http://www.diyfather.com/content/Interesting_Statistics_About_Video_Games Q9: http://www.bls.gov/tus/charts/chart16.pdf

Hypothesis test: comparing the means of affirmative responses for males vs. females total means of survey- males vs. females: 1) Null/Alternate Hypotheses Ho: males answered “yes” to the questions more than females did Ha: males did not answer “yes” to the questions more than females did 2) Conditions/Assumptions -Randomness: data was randomly selected and assorted (out of a hat) - !0%: less than 10 % of students at Baldwin Park High school were surveyed -Nearly Normal: we can assume the distribution is evenly distributed. 3) Name the Test: 2 sample T-Test 4) Do the Math p=.943 (yes) x=115 n=122 t= X1-X2/ ( √(S1^2/N1 + S2^2/N2) t= 3.015-3.086/ ( √(3.944/65 + 3.763/58) t= -.10211 p=.459 5) Conclusion Such a high p-value suggests that we do not reject the null hypothesis that males answered yes to more survey questions than females.

Chi^2 test: Do grade levels have different opinions? Q1: Ho: Liking Pokemon is independent of grade level. Ha: Liking Pokemon is dependent on grade level. Observed: Expected: Freshman Sophomores Juniors Seniors Freshman Sophomores Juniors Seniors Yes No Yes No Chi ²= 3.638 P= .3033 Because our p-value is so high, we do not reject the null hypothesis that liking Pokemon is independent of grade level. 8 18 13 50 5 6 7 15 7.033 18.967 17.041 45.959 2.98 8.025 5.95 16.049

Chi^2 test: Do grade levels have different opinions? Q2: Ho: Watching TV is independent of grade level. Ha: Watching TV is dependent on grade level. Observed: Expected: Freshman Sophomores Juniors Seniors Freshman Sophomores Juniors Seniors Yes No Yes No Chi ²= 2.303 P= .5119 Because our p-value is so high, we do not reject the null hypothesis and conclude that watching TV is independent of grade level. 1 25 5 58 1 10 0 22 1.492 24.508 3.615 59.385 .631 10.369 0 20.738

Chi^2 test: Do grade levels have different opinions? Q3: Ho: Owning a laptop is independent of grade level. Ha: Owning a laptop is dependent on grade level. Observed: Expected: Freshman Sophomores Juniors Seniors Freshman Sophomores Juniors Seniors Yes No Yes No Chi ²=.652 P= .88451 Because we have such a high p-value, we do not reject the null hypothesis and conclude that owning a laptop is independent of grade level. 13 13 26 37 5 6 9 13 11.295 14.705 27.369 35.631 4.779 6.221 9.557 12.443

Chi^2 test: Do grade levels have different opinions? Q4: Ho: Thinking that teachers should assign homework is independent of grade level. Ha: Thinking teachers should assign homework is dependent on grade level. Observed: Expected: Freshman Sophomores Juniors Seniors Freshman Sophomores Juniors Seniors Yes No Yes No Chi ²= 6.224 P= .101 Because of our high p-value, we do not reject that the thought that teachers should assign homework is independent of grade level. 16 10 28 35 8 3 15 7 14.279 11.721 34.598 28.402 6.041 4.959 12.082 9.918

Chi^2 test: Do grade levels have different opinions? Q5: Ho: Owning a smartphone is independent of grade level. Ha: Owning a smartphone is dependent on grade level. Observed: Expected: Freshman Sophomores Juniors Seniors Freshman Sophomores Juniors Seniors Yes No Yes No Chi ²= .3731 P= .946 Because of the high p-value, we do not reject the null hypothesis that owning a smartphone is independent of grade level. All grade levels DO have different opinions. 18 8 42 21 8 3 16 6 17.902 8.098 43.377 19.623 7.574 3.426 15.148 6.852

Ap stats survey project

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